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Question:

A small signal voltage V(t) = V₀sinωt is applied across an ideal capacitor C. Then:

current I(t) leads voltage V(t) by 180o

current I(t), lags voltage V(t) by 90o

over a full cycle the capacitor C does not consume any energy from the voltage source

current I(t) is in phase with voltage V(t)

Solution:

Power, P = VrmsIrmscosφ ⇒ cosφ = 0 (as φ = 90° between Irms and Vrms across a capacitor)
Therefore, power consumed = 0 in one complete cycle across a capacitor.